1. Field of the Invention
The present invention relates to a photoacoustic imaging method used in a photoacoustic imaging apparatus.
2. Description of the Related Art
The study of an optical imaging apparatus for obtaining information inside a specimen such as a living body by using the light irradiated from a light source such as a laser is actively advanced in medical fields. As one such optical imaging technique, there has been proposed photoacoustic tomography (PAT). Photoacoustic tomography is a technique in which acoustic waves generated from a living body (biological) tissue, which has absorbed the energy of light propagated and diffused in the interior of a specimen, are detected at a plurality of locations surrounding the specimen, and in which the signals thus obtained are subjected to mathematical analysis processing to visualize the information related to optical property values in the interior of the specimen. As a result of this, various information such as an initial pressure distribution, an optical energy absorption density distribution produced by light irradiation, etc., can be obtained, and these kinds of information can be applied to pinpointing the location of a malignant tumor accompanied by the multiplication of newly formed blood vessels, etc. The photoacoustic effect is a phenomenon in which, when pulsed light is shone on an object to be measured, an acoustic wave is generated due to the volume expansion in a region where the absorption coefficient is high inside the object to be measured. The acoustic wave generated due to the volume expansion by pulsed light irradiation is also called “a photoacoustic wave” in the present disclosure.
In general, in photoacoustic tomography, with respect to a specimen, at a variety of points on a closed spatial surface which encloses the entire specimen, in particular a spherical-shaped measurement surface, if the temporal change of an acoustic wave can be measured by the use of ideal sound detectors (of a wide band and point detection), an initial pressure distribution produced by light irradiation can be thoroughly reconstructed in a theoretical point of view. In addition, it is mathematically known that even in the case of a non-closed space, if measurement can be made in a cylindrical or planar manner with respect to the specimen, an initial pressure distribution produced by light irradiation can be substantially reconstructed (see Non-Patent Literature (NPL) 1).
The following equation (1) is a partial differential equation for PAT, and it is called a “photoacoustic wave equation”. If this equation is solved, acoustic wave propagation from the initial pressure distribution can be described, so that it is possible to theoretically calculate in which places and in what manner an acoustic wave can be detected:
                                          (                                                            ∇                  2                                ⁢                                  -                                      1                                          c                      2                                                                                  ⁢                                                ∂                  2                                                  ∂                                      t                    2                                                                        )                    ⁢                      p            ⁡                          (                              r                ,                t                            )                                      =                              -                                          p                0                            ⁡                              (                r                )                                              ⁢                                    ∂                              δ                ⁡                                  (                  t                  )                                                                    ∂              t                                                          (        1        )            where r is location, t is time, p(r, t) is the temporal change of the sound pressure distribution, p0(r) is the initial pressure distribution, and c is the speed of sound. δ(t) is a delta function representing the shape of a light pulse.
On the other hand, an image reconstruction of PAT is to derive the initial pressure distribution p0(r) from the sound pressure pd(rd, t) obtained at a detection point, and it is mathematically called an inverse problem. In the following, a universal back projection (UBP) method representatively used in the image reconstruction technique of PAT will be explained. In analyzing the photoacoustic wave equation in the form of equation (1) above on a frequency space, the inverse problem of calculating p0(r) can be solved in an accurate manner. The UBP represents the result thereof on a time space. The equation finally derived is as follows:
                                          p            0                    ⁡                      (            r            )                          =                              -                          2                              Ω                0                                              ⁢                      ∇                          ·                                                ∫                                      S                    0                                                  ⁢                                                                            n                      ⋒                                        0                    S                                    ⁢                                                                          ⁢                  d                  ⁢                                                                          ⁢                                                                                    S                        0                                            ⁡                                              [                                                                                                            p                              0                                                        ⁡                                                          (                                                                                                r                                  0                                                                ,                                t                                                            )                                                                                t                                                ]                                                                                    t                      =                                                                                                r                          -                                                      r                            0                                                                                                                                                                                                                              (        2        )            where Ω0 is the solid angle of an entire measuring area S0 with respect to an arbitrary reconstruction voxel (or focus point). Moreover, transforming the equation plainly and simply results in the following equation:
                                          p            0                    ⁡                      (            r            )                          =                              ∫                          Ω              0                                ⁢                                    b              ⁡                              (                                                      r                    0                                    ,                                      t                    =                                                                                        r                        -                                                  r                          0                                                                                                                                          )                                      ⁢                                                  ⁢                                          d                ⁢                                                                  ⁢                                  Ω                  0                                                            Ω                0                                                                        (        3        )            where b(r0, t) is projection data, and dΩ0 is the solid angle subtended by a detector area dS0 with respect to an arbitrary observation point P. The initial pressure distribution p0(r) can be obtained by performing back projection of the projection data according to the integration of equation (3).
Here, note that b(r0, t) and dΩ0 are as follows:
                              b          ⁡                      (                                          r                0                            ,              t                        )                          =                              2            ⁢                          p              ⁡                              (                                                      r                    0                                    ,                  t                                )                                              -                      2            ⁢            t            ⁢                                          ∂                                  p                  ⁡                                      (                                                                  r                        0                                            ,                      t                                        )                                                                              ∂                t                                                                        (        4        )                                          d          ⁢                                          ⁢                      Ω            0                          =                                            d              ⁢                                                          ⁢                              S                0                                                                                                      r                  -                                      r                    0                                                                              2                                ⁢          cos          ⁢                                          ⁢          θ                                    (        5        )            where θ is an angle which is formed by the detector and the arbitrary observation point P. In the case where the distance between a sound source and a measuring point is large enough in comparison with the size of the sound source (acoustic far-field approximation), the following relation results:
                              p          ⁡                      (                                          r                0                            ,              t                        )                          ⁢                  <<          t                ⁢                              ∂                          p              ⁡                              (                                                      r                    0                                    ,                  t                                )                                                          ∂            t                                              (        6        )            where b(r0, t) becomes as follows:
                              b          ⁡                      (                                          r                0                            ,              t                        )                          =                              -            2                    ⁢          t          ⁢                                    ∂                              p                ⁡                                  (                                                            r                      0                                        ,                    t                                    )                                                                    ∂              t                                                          (        7        )            
Thus, in such an image reconstruction of PAT, it is known that the initial pressure distribution p0(r) can be calculated by obtaining projection data b(r0, t) by performing the time differentiation of the detection signal p(r0, t) acquired by the detector, and performing the back projection of the projection data thus obtained according to equation (3) (see NPL 1 and NPL 2).    [NPL1] Physical Review E 71, 016706 (2005)    [NPL2] Review of Scientific Instruments, 77, 041101 (2006)